Abstract

In this work we construct self-adjoint extensions of the Dirac operator associated to Hermitian matrix potentials with Coulomb decay and prove that the domain is maximal. The result is obtained by means of a Hardy-Dirac type inequality. In particular, we can work with some electromagnetic potentials such that both, the electric potential and the magnetic one, have Coulomb type singularity.

Received 03 December 2012Accepted 18 March 2013Published online 08 April 2013

Acknowledgments:

The authors would like to thank M. J. Esteban and N. Visciglia for many enlightening conversations. The authors are supported in part by Grant No. MTM2011-24054 of the Ministerio de Economía y Competitividad (Spain).